Authors: Daniele Colosi (ENES-Morelia-UNAM) and Robert Oeckl (CCM-UNAM)
Year: 2020

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations which occur generically on timelike hypersurfaces in Lorentzian spacetimes as has been shown recently. We achieve this in two ways: On the one hand we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.

Authors: Daniele Colosi (ENES-Morelia-UNAM), Robert Oeckl (CCM-UNAM)
Year: 2021

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is quantized, but also the evanescent sector, with the correct physical vacuum. This yields for the first time a description of the quanta of the evanescent field alone. The key tool is the novel α-Kähler quantization prescription based on a ∗-twisted observable algebra. The spatial evolution of states between timelike hyperplanes is established and turns out to be non-unitary if different choices are made for the quantization ambiguity for initial and final hyperplane. Nevertheless, a consistent notion of transition probability is established also in the non-unitary case, thanks to the use of the positive formalism. Finally, it is shown how a conducting boundary condition on the timelike hyperplane gives rise to what we call the Casimir state. This is a pseudo-state which can be interpreted as an alternative vacuum and which gives rise to a sea of particle pairs even in this static case.

Authors: Robert Oeckl
Year: 2021

Massive Klein-Gordon theory is quantized on the timelike hypercylinder in Minkowski space. Crucially, not only the propagating, but also the evanescent sector of phase space is included, laying in this way foundations for a quantum scattering theory of fields at finite distance. To achieve this, the novel α-Kähler quantization scheme is employed in the framework of general boundary quantum field theory. A potential quantization ambiguity is fixed by stringent requirements, leading to a unitary radial evolution. Formulas for building scattering amplitudes and correlation functions are exhibited.